Hello everyone,
I am trying to work out how to complete a DiD analysis with Difference GMM and System GMM (xtabond and xtdpdsys) using Panel Data.
My data set contains 8,232 students in a Panel Data format with T=5. For each student, I have the test scores (depvar) and a list of observed variables over the time period (indepvar).
During the time series (2003-2008), a policy change is implemented in state schools in year 2007. Then, students from state schools are my treatment group and students from municipal schools are the control group. My DiD is 1 if student is enrolled in state school (treated) in post-treatment period (time).
FIRST QUESTION.
I include a lagged variable in the model with the test score of the student i in t-1. Then I need to fit the DiD in xtabond, xtdpd and xtdpdsys.
My first attempt was:
My second try was:
But I am not sure, whether the DiD in this case will work exactly in the same way as in a linear model. I need help with the implentation of DiD in this GMM and with the Interpretation of its coefficient.
SECOND QUESTION:
I assume that the schools are able to select the students based on their previous scores. In a linear model, I would include a school fixed effect in the model such as:
However, when I include the school fixed effect in the GMM, the estimation of xtabond will omit automatically some schools, and consequently, I will not be able to estimate the Sargar and Arellano-Bond Tests.
Is there someone who can help me with the inclusion of this school fixed effect using xtabond, xtdpd or xtdpdsys?
I am trying to work out how to complete a DiD analysis with Difference GMM and System GMM (xtabond and xtdpdsys) using Panel Data.
My data set contains 8,232 students in a Panel Data format with T=5. For each student, I have the test scores (depvar) and a list of observed variables over the time period (indepvar).
During the time series (2003-2008), a policy change is implemented in state schools in year 2007. Then, students from state schools are my treatment group and students from municipal schools are the control group. My DiD is 1 if student is enrolled in state school (treated) in post-treatment period (time).
FIRST QUESTION.
I include a lagged variable in the model with the test score of the student i in t-1. Then I need to fit the DiD in xtabond, xtdpd and xtdpdsys.
My first attempt was:
Code:
.
xtdpd profic_mat L.profic_mat DiD time treated $ControlVar, div($ControlVar) dgmmiv(profic_mat)
Dynamic panel-data estimation Number of obs = 9882
Group variable: IDaluno Number of groups = 4513
Time variable: wave
Obs per group: min = 1
avg = 2.189674
max = 4
Number of instruments = 14 Wald chi2(11) = 617.96
Prob > chi2 = 0.0000
One-step results
------------------------------------------------------------------------------
profic_mat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
profic_mat |
L1. | 1.647524 .1168507 14.10 0.000 1.418501 1.876547
|
DiD | 430.7909 228.7262 1.88 0.060 -17.50425 879.0861
time | -222.3807 108.4029 -2.05 0.040 -434.8464 -9.915043
treated | -562.5099 1232.334 -0.46 0.648 -2977.841 1852.821
q111 | -68.1603 29.99675 -2.27 0.023 -126.9529 -9.367746
educaTeach | -8.906975 8.316335 -1.07 0.284 -25.20669 7.392742
q110 | -5.890573 2.960751 -1.99 0.047 -11.69354 -.087607
q108 | 4.331367 3.963205 1.09 0.274 -3.436371 12.09911
q106 | 1.783682 2.607462 0.68 0.494 -3.32685 6.894214
q105 | -9.611421 4.845548 -1.98 0.047 -19.10852 -.114321
q104 | -14.47452 4.744586 -3.05 0.002 -23.77374 -5.175307
_cons | 453.0812 713.6051 0.63 0.525 -945.5591 1851.722
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/.).profic_mat
Standard: D.q111 D.educaTeach D.q110 D.q108 D.q106 D.q105 D.q104
Instruments for level equation
Standard: _cons
My second try was:
Code:
.
xtdpd profic_mat L.profic_mat DiD time treated $ControlVar, div(DiD time treated $ControlVar) dgmmiv(profic_mat)
Dynamic panel-data estimation Number of obs = 9882
Group variable: IDaluno Number of groups = 4513
Time variable: wave
Obs per group: min = 1
avg = 2.189674
max = 4
Number of instruments = 17 Wald chi2(11) = 2530.95
Prob > chi2 = 0.0000
One-step results
------------------------------------------------------------------------------
profic_mat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
profic_mat |
L1. | 1.531564 .0536515 28.55 0.000 1.426409 1.636718
|
DiD | -3.456692 3.764445 -0.92 0.358 -10.83487 3.921484
time | -15.46012 3.739152 -4.13 0.000 -22.78873 -8.131519
treated | -7.031441 16.22298 -0.43 0.665 -38.8279 24.76502
q111 | -6.463428 5.720106 -1.13 0.258 -17.67463 4.747773
educaTeach | 1.322595 2.059962 0.64 0.521 -2.714857 5.360048
q110 | -2.258975 .8237047 -2.74 0.006 -3.873406 -.6445432
q108 | -.8757389 1.042708 -0.84 0.401 -2.919409 1.167931
q106 | 1.828283 .9248911 1.98 0.048 .0155295 3.641036
q105 | -3.568163 1.739991 -2.05 0.040 -6.978484 -.1578426
q104 | -7.057929 1.010115 -6.99 0.000 -9.037717 -5.07814
_cons | 4.549558 18.15347 0.25 0.802 -31.03059 40.12971
------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/.).profic_mat
Standard: D.DiD D.time D.treated D.q111 D.educaTeach D.q110 D.q108 D.q106 D.q105 D.q104
Instruments for level equation
Standard: _cons
But I am not sure, whether the DiD in this case will work exactly in the same way as in a linear model. I need help with the implentation of DiD in this GMM and with the Interpretation of its coefficient.
SECOND QUESTION:
I assume that the schools are able to select the students based on their previous scores. In a linear model, I would include a school fixed effect in the model such as:
Code:
xtreg profic_mat DiD time treated i.IDescola $controlVar, fe robust
Is there someone who can help me with the inclusion of this school fixed effect using xtabond, xtdpd or xtdpdsys?
Code:
xi: xtabond profic_mat i.IDescola $controlVar
i.IDescola _IIDescola_35018107-35924957(naturally coded; _IIDescola_35018107 omitted)
note: _IIDescola_35018348 dropped from div() because of collinearity
note: _IIDescola_35042648 dropped from div() because of collinearity
note: _IIDescola_35047193 dropped from div() because of collinearity
note: _IIDescola_35083823 dropped from div() because of collinearity
note: _IIDescola_35091455 dropped from div() because of collinearity
note: _IIDescola_35121009 dropped from div() because of collinearity
note: _IIDescola_35802062 dropped from div() because of collinearity
note: _IIDescola_35909397 dropped from div() because of collinearity
Arellano-Bond dynamic panel-data estimation Number of obs = 8688
Group variable: IDaluno Number of groups = 3948
Time variable: wave
Obs per group: min = 1
avg = 2.200608
max = 3
Number of instruments = 51 Wald chi2(45) = 7598.99
Prob > chi2 = 0.0000
One-step results
-------------------------------------------------------------------------------------
profic_mat | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
profic_mat |
L1. | 1.258465 .014629 86.03 0.000 1.229793 1.287137
|
_IIDescola_35018348 | 0 (omitted)
_IIDescola_35018387 | -146.5501 125.1708 -1.17 0.242 -391.8803 98.78011
_IIDescola_35018399 | -56.21933 138.8311 -0.40 0.686 -328.3232 215.8845
_IIDescola_35018485 | 0 (omitted)
_IIDescola_35018512 | -56.97495 128.5957 -0.44 0.658 -309.0179 195.068
_IIDescola_35018824 | -4.880865 131.7323 -0.04 0.970 -263.0715 253.3097
_IIDescola_35042648 | 0 (omitted)
_IIDescola_35047193 | 0 (omitted)
_IIDescola_35059122 | -10.78363 152.7991 -0.07 0.944 -310.2644 288.6971
_IIDescola_35059158 | -109.8035 132.0008 -0.83 0.405 -368.5204 148.9133
_IIDescola_35059161 | 13.41882 138.4068 0.10 0.923 -257.8536 284.6912
_IIDescola_35059171 | -32.64202 135.8725 -0.24 0.810 -298.9473 233.6633
_IIDescola_35059213 | -76.52402 123.3575 -0.62 0.535 -318.3003 165.2523
_IIDescola_35059225 | -59.65258 134.0156 -0.45 0.656 -322.3183 203.0131
_IIDescola_35059237 | -80.45224 138.1547 -0.58 0.560 -351.2306 190.3261
_IIDescola_35071122 | 0 (omitted)
_IIDescola_35083811 | -32.95767 137.9087 -0.24 0.811 -303.2538 237.3385
_IIDescola_35083823 | 0 (omitted)
_IIDescola_35083847 | -52.87668 132.9422 -0.40 0.691 -313.4387 207.6853
_IIDescola_35083859 | 177.9229 90.17332 1.97 0.048 1.186421 354.6593
_IIDescola_35083860 | -53.44163 149.6163 -0.36 0.721 -346.6841 239.8009
_IIDescola_35084153 | -169.6971 140.5855 -1.21 0.227 -445.2397 105.8455
_IIDescola_35086236 | -45.69124 142.6483 -0.32 0.749 -325.2768 233.8943
_IIDescola_35088614 | -136.5818 138.9607 -0.98 0.326 -408.9398 135.7762
_IIDescola_35088648 | -120.5696 150.5347 -0.80 0.423 -415.6123 174.473
_IIDescola_35088675 | 0 (omitted)
_IIDescola_35088705 | -95.6 63.77123 -1.50 0.134 -220.5893 29.38931
_IIDescola_35091455 | 0 (omitted)
_IIDescola_35112513 | -80.03572 90.17316 -0.89 0.375 -256.7719 96.70043
_IIDescola_35112641 | -5.148722 138.8601 -0.04 0.970 -277.3095 267.0121
_IIDescola_35112859 | 0 (omitted)
_IIDescola_35112872 | -89.89423 120.794 -0.74 0.457 -326.6462 146.8577
_IIDescola_35121009 | 0 (omitted)
_IIDescola_35123067 | -183.3962 127.9934 -1.43 0.152 -434.2587 67.4662
_IIDescola_35123080 | -72.52996 121.0912 -0.60 0.549 -309.8644 164.8045
_IIDescola_35126846 | -173.7891 137.0818 -1.27 0.205 -442.4644 94.8863
_IIDescola_35131994 | -68.76753 124.6852 -0.55 0.581 -313.1461 175.611
_IIDescola_35132263 | -78.41009 110.4183 -0.71 0.478 -294.8261 138.0059
_IIDescola_35138769 | -118.0649 152.9151 -0.77 0.440 -417.773 181.6432
_IIDescola_35140636 | -130.9619 165.691 -0.79 0.429 -455.7104 193.7865
_IIDescola_35156590 | -99.10153 122.5745 -0.81 0.419 -339.3431 141.14
_IIDescola_35159955 | 16.42608 140.0503 0.12 0.907 -258.0675 290.9197
_IIDescola_35162024 | -40.49048 138.9536 -0.29 0.771 -312.8346 231.8536
_IIDescola_35172467 | -25.56766 63.76831 -0.40 0.688 -150.5513 99.41592
_IIDescola_35172510 | -109.1299 123.4419 -0.88 0.377 -351.0716 132.8118
_IIDescola_35172716 | 0 (omitted)
_IIDescola_35185103 | 0 (omitted)
_IIDescola_35283685 | -32.08828 135.2679 -0.24 0.812 -297.2086 233.032
_IIDescola_35802062 | 0 (omitted)
_IIDescola_35901124 | -55.04499 135.3391 -0.41 0.684 -320.3048 210.2149
_IIDescola_35901143 | 0 (omitted)
_IIDescola_35903917 | -94.51909 129.5968 -0.73 0.466 -348.5242 159.4861
_IIDescola_35905446 | -112.2985 128.4339 -0.87 0.382 -364.0244 139.4274
_IIDescola_35907397 | -88.9827 137.7691 -0.65 0.518 -359.0052 181.0398
_IIDescola_35909397 | 0 (omitted)
_IIDescola_35913005 | 38.66991 138.4898 0.28 0.780 -232.7652 310.105
_IIDescola_35913923 | 0 (omitted)
_IIDescola_35914885 | -173.8479 137.4867 -1.26 0.206 -443.3169 95.62119
_IIDescola_35924945 | -107.2916 136.3635 -0.79 0.431 -374.5591 159.9758
_IIDescola_35924957 | -1.89335 63.76368 -0.03 0.976 -126.8679 123.0812
_cons | 48.8823 87.6766 0.56 0.577 -122.9607 220.7253
-------------------------------------------------------------------------------------
Instruments for differenced equation
GMM-type: L(2/.).profic_mat
Standard: D._IIDescola_35018387 D._IIDescola_35018399 D._IIDescola_35018485 D._IIDescola_35018512 D._IIDescola_35018824
D._IIDescola_35059122 D._IIDescola_35059158 D._IIDescola_35059161 D._IIDescola_35059171 D._IIDescola_35059213
D._IIDescola_35059225 D._IIDescola_35059237 D._IIDescola_35071122 D._IIDescola_35083811 D._IIDescola_35083847
D._IIDescola_35083859 D._IIDescola_35083860 D._IIDescola_35084153 D._IIDescola_35086236 D._IIDescola_35088614
D._IIDescola_35088648 D._IIDescola_35088675 D._IIDescola_35088705 D._IIDescola_35112513 D._IIDescola_35112641
D._IIDescola_35112859 D._IIDescola_35112872 D._IIDescola_35123067 D._IIDescola_35123080 D._IIDescola_35126846
D._IIDescola_35131994 D._IIDescola_35132263 D._IIDescola_35138769 D._IIDescola_35140636 D._IIDescola_35156590
D._IIDescola_35159955 D._IIDescola_35162024 D._IIDescola_35172467 D._IIDescola_35172510 D._IIDescola_35172716
D._IIDescola_35185103 D._IIDescola_35283685 D._IIDescola_35901124 D._IIDescola_35901143 D._IIDescola_35903917
D._IIDescola_35905446 D._IIDescola_35907397 D._IIDescola_35913005 D._IIDescola_35913923 D._IIDescola_35914885
D._IIDescola_35924945 D._IIDescola_35924957
Instruments for level equation
Standard: _cons
.
end of do-file
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